# Amir Hossein

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bio website location Arak, Iran age 20 member for 3 years, 10 months seen Aug 25 at 8:38 profile views 873

Electrical Engineering student at University of Tehran.

# 44 Questions

 88 All polynomials with no natural roots and integer coefficients such that $\phi(n)|\phi(P(n))$ 22 An information theory inequality which relates to Shannon Entropy 17 Showing $\tan\frac{2\pi}{13}\tan\frac{5\pi}{13}\tan\frac{6\pi}{13}=\sqrt{65+18\sqrt{13}}$ 15 The easy(?) part of IMO 2011 Problem 3 14 $x,y$ are integers satisfying $2x^2-1=y^{15}$, show that $5 \mid x$

# 1,868 Reputation

 +10 Proving $2 ( \cos \frac{4\pi}{19} + \cos \frac{6\pi}{19}+\cos \frac{10\pi}{19} )$ is a root of$\sqrt{ 4+ \sqrt{ 4 + \sqrt{ 4-x}}}=x$ +25 All polynomials with no natural roots and integer coefficients such that $\phi(n)|\phi(P(n))$ +3 Difference between “Show” and “Prove” +5 Showing $\tan\frac{2\pi}{13}\tan\frac{5\pi}{13}\tan\frac{6\pi}{13}=\sqrt{65+18\sqrt{13}}$

 11 Alternative proof that $(a^2+b^2)/(ab+1)$ is a square when it's an integer 2 Why does a matrix have determinant zero if one row is the sum of two other rows? 2 Show $f(x)=\sqrt{x^4+1} - \sqrt{x^4+x^2} \rightarrow -1/2$ for $x \rightarrow \infty$, $x \in \mathbb R$. 1 How to answer the question from Calculus by Michael Spivak Chapter 5 Problem 14 1 Proving ${n \choose p} \equiv \Bigl[\frac{n}{p}\Bigr] \ (\text{mod} \ p)$

# 30 Tags

 12 number-theory × 30 1 limits 2 matrices × 3 0 diophantine-equations × 17 2 determinant × 2 0 elementary-number-theory × 13 2 real-analysis 0 contest-math × 5 1 calculus 0 algebra-precalculus × 4

# 8 Accounts

 Mathematics 1,868 rep 838 Server Fault 101 rep 2 TeX - LaTeX 101 rep 2 Electrical Engineering 101 rep 2 Physics 101 rep 1